What is first theorem of Pappus Galdinus?

In mathematics, Pappus’s centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus’s theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. The theorems are attributed to Pappus of Alexandria and Paul Guldin.

What is the hexagon theorem?

In projective geometry, Pascal’s theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of opposite …

What is Pappus theorem in engineering mechanics?

The Pappus–Guldin Theorems Suppose that a plane curve is rotated about an axis external to the curve. Then 1. the resulting surface area of revolution is equal to the product of the length of the curve and the displacement of its centroid; 2.

What are the theorems of Pappus and Guldinus used for?

This set of Engineering Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Theorem of Pappus and Guldinus”. Explanation: The theorem is used to find the surface area and the volume of the revolving body. Thus the surface area and the volume of any 2D curve.

What is Pascal’s theorem used for?

The intersection of chords formed by six points are collinear. Pascal’s theorem is a very useful theorem in Olympiad geometry to prove the collinearity of three intersections among six points on a circle.

What is parallel axis theorem in mechanics?

The parallel axis theorem states that. The moment of inertia of a body about an axis parallel to the body passing through its centre is equal to the sum of moment of inertia of the body about the axis passing through the centre and product of the mass of the body times the square of the distance between the two axes.

How do you use Pappus Theorem to find volume?

Using the Theorem of Pappus, we know that the volume of a right circular cone with base radius r = 6 r=6 r=6 and height h = 1 0 h=10 h=10 is V = 7 2 π 3 4 V=72\pi\sqrt{34} V=72π√​34​​​.

What is the configuration of Pappus’s hexagon theorem?

The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus’s theorem, with each line meeting 3 of the points and each point meeting 3 lines. In general, the Pappus line does not pass through the point of intersection of ABC and abc.

Which is the best proof of Pappus’s theorem?

Theorem 1.1 (Pappus’s hexagon Theorem). Let A,B,C be three points on a straight line and let X,Y,Z be three points on another line. If the lines AY , BZ, CX intersect the lines BX, CY, AZ, respectively then the three points of intersection are collinear.

How is the volume of an object determined by the theorem of Pappus?

The Theorem of Pappus tells us that the volume of a three-dimensional solid object that’s created by rotating a two-dimensional shape around an axis is given by V=Ad. V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance tr

How is P appus theorem similar to Pascal’s theorem?

P appus’ theorem looks very similar to Pascal’s hexagon theorem. In Pascal’s theorem, we have a hexagon inscribed in a circle and the intersection points of the three pairs of opposite sides of the hexagon lie on a straight line.